Connectedness Of The Boundary In The AdS/CFT Correspondence

Details Connectedness Of The Boundary In The AdS/CFT Correspondence Connectedness Of The Boundary In The AdS/CFT Correspondence

1999-10-29

arxiv.org/abs/hep-th/9910245v1

Adv.Theor.Math.Phys.3:1635-1655,1999

Physics

High Energy Physics

High Energy Physics - Theory

19 pp

Scientific paper

Let $M$ be a complete Einstein manifold of negative curvature, and assume
that (as in the AdS/CFT correspondence) it has a Penrose compactification with
a conformal boundary $N$ of positive scalar curvature. We show that under these
conditions, $H_n(M;Z)=0$ and in particular $N$ must be connected. These results
resolve some puzzles concerning the AdS/CFT correspondence.

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